Accelerometer-based tilt estimation of a rigid body with only rotational degrees of freedom

An estimation algorithm is developed for determining pitch and roll angles (tilt) of a rigid body fixed at a pivot point using multiple accelerometers. The estimate is independent of the rigid body dynamics; the method is applicable both in static conditions and for any dynamic motion of the body. No dynamic model is required for the estimator; only the mounting positions of the sensors need to be known. The proposed estimator is the optimal linear estimate in a least-squares sense if knowledge of the system dynamics is not used. The estimate may be used as a basis for further filtering and fusion techniques, such as sensor fusion with rate gyro data. The estimation algorithm is applied to the problem of state estimation for the Balancing Cube, a rigid structure that can actively balance on its corners. Experimental results are provided.